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Weakly harmonic

In mathematics, a function f is weakly harmonic in a domain D if

∫fΔg = 0
D

for all g with compact support in D and continuous second derivatives, where Δ is the Laplacian. Surprisingly, this definition is equivalent to the seemingly stronger definition. That is, f is weakly harmonic if and only if it is a harmonic function.

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10-26-2009 08:16:03
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